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Abeasis, S.; Del Fra, A.; Kraft, H.

The geometry of representations of \(A_m\). (English) Zbl 0477.14027

Math. Ann. 256, 401-418 (1981).
Reviewer: Hanspeter Kraft (Bonn)
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Cited in 3 Reviews
Cited in 18 Documents

MSC:

14M17 Homogeneous spaces and generalizations
14B07 Deformations of singularities
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
14L30 Group actions on varieties or schemes (quotients)
14M12 Determinantal varieties
14B05 Singularities in algebraic geometry
20G15 Linear algebraic groups over arbitrary fields
16Gxx Representation theory of associative rings and algebras

Keywords:

orbit closures; determinantal singularities; representations of Dynkin quiver; normal Cohen-Macaulay; rational singularities; minimal degeneration of singularities
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Full Text: DOI EuDML

References:

[1] Abeasis, S., Del Fra, A.: Degenerations for the representations of an equioriented quiver of type \[ \(\backslash\)underset\{\(\backslash\)raise0.3em\(\backslash\)hbox\{\(\smash{\scriptscriptstyle-}\)\}\}\{A\} \_m \] . Boll. Un. Mat. It. (Suppl.) Algebra e Geometria, 157–171 (1980) · Zbl 0449.16024
[2] Gabriel, P.: Unzerlegbare Darstellungen. I. manuscripta math.6, 71–103 (1972) · Zbl 0232.08001 · doi:10.1007/BF01298413
[3] Gabriel, P.: Indecomposable representations. II. Ist. Nazionale di Alta Mat. Symposia Mat.XI, 81–104 (1973)
[4] Grothendieck, A., Dieudonné, J.: EGA O-IV. Publ. Math. de l’I.H.E.S.11, 20, 24, 28, 32, Paris (1961–1967)
[5] Hesselink, W.: Singularities in the nilpotent scheme of a classical group. Trans. Am. Math. Soc.222, 1–32 (1976) · Zbl 0332.14017 · doi:10.1090/S0002-9947-1976-0429875-8
[6] Hochster, M.: Proceedings of the International Congress of Mathematicians. Helsinki, 1978 · Zbl 0421.14001
[7] Kempf, G., Knudsen, F., Mumford, D., Saint-Donat, B.: Toroidal embeddings. I. Springer Lecture Notes, Vol. 339. Berlin, Heidelberg, New York: Springer 1973 · Zbl 0271.14017
[8] Kempf, G.: Images of homogeneous vector bundles and varieties of complexes. Bull. Am. Math. Soc.81, 900–901 (1975) · Zbl 0322.14020 · doi:10.1090/S0002-9904-1975-13878-X
[9] Kempf, G.: On the collapsing of homogeneous bundles. Invent. Math.37, 229–239 (1976) · Zbl 0338.14015 · doi:10.1007/BF01390321
[10] Kraft, H., Procesi, C.: Closures of conjugacy classes of matrices are normal. Invent. Math.53, 227–247 (1979) · Zbl 0434.14026 · doi:10.1007/BF01389764
[11] Kraft, H., Procesi, C.: Minimal singularities in GLn. Invent. Math.62, 503–515 (1981) · Zbl 0478.14040 · doi:10.1007/BF01394257
[12] Mumford, D.: Geometric invariant theory. Ergebnisse der Mathematik, Vol. 34. Berlin, Heidelberg, New York: Springer 1970 · Zbl 0147.39304
[13] Procesi, C., Kraft, H.: Classi coniugate in GL(n, \(\mathbb{C}\)). Rend. Sem. Mat. Univ. Padova59, 209–222 (1978) · Zbl 0478.14039
[14] Vust, Th.: Sur la théorie des invariants des groupes classiques. Ann. Inst. Fourier (Grenoble)26, 1–31 (1976) · Zbl 0314.20035
[15] Weyl, H.: The classical groups, their invariants and representations. Princeton Mathematical Series, Vol. 1, Princeton: Princeton University Press 1946 · Zbl 1024.20502
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